Physics-embedded probabilistic model for extrapolating the electromagnetic scattering from a metal target under geometric scaling

This Letter proposes a physics-embedded Gaussian process regression (GPR), which is simultaneously high-fidelity and reliability-aware, for extrapolating the radar cross section (RCS) of a target under geometric scaling. Distinct from alternative RCS extrapolation models that operate in the RCS domain, we establish the model in the scattered electric-field domain rooted in the nature of the coherent superposition of electromagnetic waves. By designing a composite kernel that integrates a degree-2 generalized polynomial for scaling laws and a spectral mixture (SM) kernel for interference effects, we explicitly encode these physical priors into the GPR framework. Validated on a simple warhead model and the complex SLICY model, the proposed GPR reduces the root-mean-square extrapolation error by up to 91.5% compared to other alternative models, while providing physics-grounded uncertainty quantification for reliability assessment.